Successfully complete the game and save when promoted to unlock the "Game Record" and "Sound Test" options at the title screen, Unknown mode, and Very Hard mode. You can also use your cleared saved game file to start a New Game+ playthrough, which allows access to the Grade Shop, and has the following items for purchase:

1/2 Experience: 10 Grade

10x Experience: 3,000 Grade

2x Experience: 1,000 Grade

2x Gald: 600 Grade

Decrease Starting HP by 150: 10 Grade

Display Synopsis from beginning: 10 Grade

Double Grade increase and Decrease: 100 Grade

Increase Max Item Limit to 20: 400 Grade

Increase Over Limit fill speed: 450 Grade

Increase Starting HP by 500: 250 Grade

Inherit AD Skills: 900 Grade

Inherit Artes Learned: 1,000 Grade

Inherit Artes Usage: 100 Grade

Inherit Battle Info: 10 Grade

Inherit Capacity Cores: 500 Grade

Inherit Character Disc Info: 10 Grade

Inherit Collector's Book Data: 10 Grade

Inherit Cooking Ability: 50 Grade

Inherit FS Chambers: 150 Grade

Inherit Gald: 1,000 Grade

Inherit Items: 500 Grade

Inherit mini-game data: 10 Grade

Inherit Recipes: 50 Grade

Inherit Special Items: 10 Grade

Inherit Titles (including costumes): 500 Grade

Inherit World Map info: 10 Grade

Increase Combo Bonus: 50 Grade

Play Time carried over: 10 Grade

Abyss Replica Facility dungeon

Begin a New Game+ playthrough. Save Shiba, and complete the Ortion Cavern (East) side quest. Go to Sheridan, then talk to the two men in the northwest part. Talk to Shiba again, and you will be transported to the Abyss Replica Facility dungeon.

Brillante secret shop

Successfully complete the Collector's Book by finishing the game two times. Speak to the purple-dressed man at the library in the Daath church to get Jade's "Item Collector" title. Talk to him again with that title to access the Brillante secret shop near the inn in Grand Chokmah.